Sequences

Check out this list of numbers. 👇

32, 34, 36, 38, 40, 42, ...

Does it follow a pattern? 🤔

Yes! 😃 Each number goes up by 2.

Lists like this are called **sequences!**

A **sequence **is a list of numbers that follows a **pattern or rule.**

👉 Some examples of sequences are:

0, 1, 2, 3, 4, 5, ...

5, 10, 15, 20, 25, 30, ...

A sequence has **3 parts:** terms, a rule, and an ending.

** Terms **are the numbers that form a sequence.

For example, the terms of the above sequence 👆 are **0, 2, 4, 6, 8, etc.**

A **rule or pattern** is the specific order that a sequence follows.

For example, the **rule **for the above sequence 👆 is **+2.**

A sequence can stop after a few terms, or go on forever.

If a sequence goes on forever, we put **3 dots (...) **at the end, called **ellipsis.**

The dots (...) in the above sequence 👆 tell us that it goes on forever.

Here's an example of a sequence that **does not go on forever**:

4, 8, 12, 16, 20

Sequences can **count up **or** down.**

Sequences that count **up **are called **forward sequences.**

For example, this is a forward sequence:

Sequences that count **down **are called **backward sequences.**

For example, this is a backward sequence:

To find the **rule **of a sequence, just find out how to get from one term to the next.

👉 For example,

Let's try to **find the rule **of this sequence.

0, 6, 12, 18, 24, 30, ...

What happens to **0 (the first term) **to make it **6 (the second term)**?

That's right! 😃

0+ 6= 6

Similarly,

6+ 6= 12

So, the rule of this sequence is **+6.**

👉 Let's try another example.

Find the rule of this sequence.

84, 81, 78, 75, 72, ...

Where do we start?

👉We look at change between the first and second terms!

What happens to **84 **to turn it into **81?**

You got it! 🤗

84- 3= 81

So, the rule of the sequence is **-3.**

Great work! 👏

Check out this sequence.

15, 30, ____, ____, 75, 90

It's missing some terms!

How can we find them? 🤔

To **find **the **missing terms **in a sequence, first find the **rule. **Then **use it **to find the missing terms.

Let's try it!

What's the **rule **of the above sequence? 🤔

👉 To find out let's look at the first 2 terms.

15+ __= 30

To go from one term to the next, we add 15!

15+ 15= 30

So, the rule of the sequence is **+15. ✅**

Now let's **use this rule** to find the missing terms.

What comes after 30 in the sequence?

30+ 15=45

45+ 15=60

That's it! 😎

The missing terms of the sequence are** 45 and 60.**

15, 30, 45, 60, 75, 90

Great job! 🎉

Now you're ready to ace some practice questions.

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